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Currently displaying 1 – 3 of 3

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A proof of the crossing number of $K_{3, n}$ in a surface

Pak Tung Ho — 2007

Discussiones Mathematicae Graph Theory

In this note we give a simple proof of a result of Richter and Siran by basic counting method, which says that the crossing number of $K_{3, n}$ in a surface with Euler genus ε is ⎣n/(2ε+2)⎦ n - (ε+1)(1+⎣n/(2ε+2)⎦).

The projective plane crossing number of the circulant graph C(3k;{1,k})

Pak Tung Ho — 2012

Discussiones Mathematicae Graph Theory

In this paper we prove that the projective plane crossing number of the circulant graph C(3k;{1,k}) is k-1 for k ≥ 4, and is 1 for k = 3.

Squares in $(1^{2} + m^{2}) \dots (n^{2} + m^{2})$ .

Ho, Pak Tung — 2009

Integers

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